Fast Point Spread Function Modeling with Deep Learning

Modeling the Point Spread Function (PSF) of wide-field surveys is vital for many astrophysical applications and cosmological probes including weak gravitational lensing. The PSF smears the image of any recorded object and therefore needs to be taken into account when inferring properties of galaxies from astronomical images. In the case of cosmic shear, the PSF is one of the dominant sources of systematic errors and must be treated carefully to avoid biases in cosmological parameters. Recently, forward modeling approaches to calibrate shear measurements within the Monte-Carlo Control Loops ($MCCL$) framework have been developed. These methods typically require simulating a large amount of wide-field images, thus, the simulations need to be very fast yet have realistic properties in key features such as the PSF pattern. Hence, such forward modeling approaches require a very flexible PSF model, which is quick to evaluate and whose parameters can be estimated reliably from survey data. We present a PSF model that meets these requirements based on a fast deep-learning method to estimate its free parameters. We demonstrate our approach on publicly available SDSS data. We extract the most important features of the SDSS sample via principal component analysis. Next, we construct our model based on perturbations of a fixed base profile, ensuring that it captures these features. We then train a Convolutional Neural Network to estimate the free parameters of the model from noisy images of the PSF. This allows us to render a model image of each star, which we compare to the SDSS stars to evaluate the performance of our method. We find that our approach is able to accurately reproduce the SDSS PSF at the pixel level, which, due to the speed of both the model evaluation and the parameter estimation, offers good prospects for incorporating our method into the $MCCL$ framework.Comment: 25 pages, 8 figures, 1 tabl

Spectro-Imaging Forward Model of Red and Blue Galaxies

For the next generation of spectroscopic galaxy surveys, it is important to forecast their performances and to accurately interpret their large data sets. For this purpose, it is necessary to consistently simulate different populations of galaxies, in particular Emission Line Galaxies (ELGs), less used in the past for cosmological purposes. In this work, we further the forward modeling approach presented in Fagioli et al. 2018, by extending the spectra simulator Uspec to model galaxies of different kinds with improved parameters from Tortorelli et al. 2020. Furthermore, we improve the modeling of the selection function by using the image simulator Ufig. We apply this to the Sloan Digital Sky Survey (SDSS), and simulate $\sim157,000$ multi-band images. We pre-process and analyse them to apply cuts for target selection, and finally simulate SDSS/BOSS DR14 galaxy spectra. We compute photometric, astrometric and spectroscopic properties for red and blue, real and simulated galaxies, finding very good agreement. We compare the statistical properties of the samples by decomposing them with Principal Component Analysis (PCA). We find very good agreement for red galaxies and a good, but less pronounced one, for blue galaxies, as expected given the known difficulty of simulating those. Finally, we derive stellar population properties, mass-to-light ratios, ages and metallicities, for all samples, finding again very good agreement. This shows how this method can be used not only to forecast cosmology surveys, but it is also able to provide insights into studies of galaxy formation and evolution.Comment: 28 pages, 10 figures, accepted for publication in JCA

Fast Lightcones for Combined Cosmological Probes

The combination of different cosmological probes offers stringent tests of the $\Lambda$CDM model and enhanced control of systematics. For this purpose, we present an extension of the lightcone generator UFalcon first introduced in Sgier et al. 2019 (arXiv:1801.05745), enabling the simulation of a self-consistent set of maps for different cosmological probes. Each realization is generated from the same underlying simulated density field, and contains full-sky maps of different probes, namely weak lensing shear, galaxy overdensity including RSD, CMB lensing, and CMB temperature anisotropies from the ISW effect. The lightcone generation performed by UFalcon is parallelized and based on the replication of a large periodic volume simulated with the GPU-accelerated $N$-Body code PkdGrav3. The post-processing to construct the lightcones requires only a runtime of about 1 walltime-hour corresponding to about 100 CPU-hours. We use a randomization procedure to increase the number of quasi-independent full-sky UFalcon map-realizations, which enables us to compute an accurate multi-probe covariance matrix. Using this framework, we forecast cosmological parameter constraints by performing a multi-probe likelihood analysis for a combination of simulated future stage-IV-like surveys. We find that the inclusion of the cross-correlations between the probes significantly increases the information gain in the parameter constraints. We also find that the use of a non-Gaussian covariance matrix is increasingly important, as more probes and cross-correlation power spectra are included. A version of the UFalcon package currently including weak gravitational lensing is publicly available.Comment: 49 pages, 24 pictures, The UFalcon weak lensing package is available here: $\href{https://cosmology.ethz.ch/research/software-lab/UFalcon.html}{https://cosmology.ethz.ch/research/software-lab/UFalcon.html}

Forward Modeling of Spectroscopic Galaxy Surveys: Application to SDSS

Galaxy spectra are essential to probe the spatial distribution of galaxies in our Universe. To better interpret current and future spectroscopic galaxy redshift surveys, it is important to be able to simulate these data sets. We describe Uspec, a forward modeling tool to generate galaxy spectra taking into account some intrinsic galaxy properties as well as instrumental responses of a given telescope. The model for the intrinsic properties of the galaxy population, i.e., the luminosity functions, and size and spectral coefficients distribu- tions, was developed in an earlier work for broad-band imaging surveys [1], and we now aim to test the model further using spectroscopic data. We apply Uspec to the SDSS/CMASS sample of Luminous Red Galaxies (LRGs). We construct selection cuts that match those used to build this LRG sample, which we then apply to data and simulations in the same way. The resulting real and simulated average spectra show a good statistical agreement overall, with residual differences likely coming from a bluer galaxy population of the simulated sam- ple. We also do not explore the impact of non-solar element ratios in our simulations. For a quantitative comparison, we perform Principal Component Analysis (PCA) of the sets of spectra. By comparing the PCs constructed from simulations and data, we find good agree- ment for all components. The distributions of the eigencoefficients also show an appreciable overlap. We are therefore able to properly simulate the LRG sample taking into account the SDSS/BOSS instrumental responses. The differences between the two samples can be ascribed to the intrinsic properties of the simulated galaxy population, which can be reduced by further improvements of our modelling method in the future. We discuss how these results can be useful for the forward modeling of upcoming large spectroscopic surveys.Comment: 32 pages, 14 figures, accepted by JCA

The PAU Survey: A Forward Modeling Approach for Narrow-band Imaging

Weak gravitational lensing is a powerful probe of the dark sector, once measurement systematic errors can be controlled. In Refregier & Amara (2014), a calibration method based on forward modeling, called MCCL, was proposed. This relies on fast image simulations (e.g., UFig; Berge et al. 2013) that capture the key features of galaxy populations and measurement effects. The MCCL approach has been used in Herbel et al. (2017) to determine the redshift distribution of cosmological galaxy samples and, in the process, the authors derived a model for the galaxy population mainly based on broad-band photometry. Here, we test this model by forward modeling the 40 narrow-band photometry given by the novel PAU Survey (PAUS). For this purpose, we apply the same forced photometric pipeline on data and simulations using Source Extractor (Bertin & Arnouts 1996). The image simulation scheme performance is assessed at the image and at the catalogues level. We find good agreement for the distribution of pixel values, the magnitudes, in the magnitude-size relation and the interband correlations. A principal component analysis is then performed, in order to derive a global comparison of the narrow-band photometry between the data and the simulations. We use a `mixing' matrix to quantify the agreement between the observed and simulated sets of Principal Components (PCs). We find good agreement, especially for the first three most significant PCs. We also compare the coefficients of the PCs decomposition. While there are slight differences for some coefficients, we find that the distributions are in good agreement. Together, our results show that the galaxy population model derived from broad-band photometry is in good overall agreement with the PAUS data. This offers good prospect for incorporating spectral information to the galaxy model by adjusting it to the PAUS narrow-band data using forward modeling.Comment: Submitted to JCAP, 28 pages, 15 figures, 3 appendice

A forward-modeling approach to cosmic shear

The current cosmological concordance model, ΛCDM, is very successful at describing the statistical properties of the Universe and its evolution with cosmic time at both low and high redshifts. However, two major ingredients of ΛCDM, cold dark matter (CDM) and dark energy (Λ), are only phenomenologically motivated and cosmologists lacks deeper understanding of their origins. Therefore, investigating the physical nature of this dark sector of the ΛCDM model is one of the most pressing issues in modern cosmology and multiple major observational programs aimed at investigating the dark components of ΛCDM are either on the way or already in operation. At low redshifts, three major wide-field surveys, the Kilo-Degree Survey (KiDS), the Dark Energy Survey (DES) and the Hyper Suprime-Cam (HSC) survey, have recently published updated cosmology constraints. They all rely on cosmic shear, the weak gravitational lensing by large-scale structures, as a powerful probe of both the expansion history of the Universe and the growth of structures. While cosmic shear has great potential to shine light on the dark sector of ΛCDM, the effect is challenging to measure and prone to systematic effects. Therefore, Refregier & Amara (2014, DOI: 10.1016/j.dark.2014.01.002) proposed the Monte-Carlo Control Loops (MCCL) framework. This method employs large amounts of forward simulations to quantify the systematic uncertainty of cosmic shear measurements and propagate it through the analysis in a probabilistic way. In this thesis, we develop methods for measuring cosmology with cosmic shear based on the MCCL framework. We first implement and test a forward-modeling approach to measuring the redshift distribution n(z) of typical weak lensing samples. To this end, we devise an empirical model of the intrinsic galaxy population based on redshift-dependent luminosity functions. We then use Approximate Bayesian Computation (ABC) to adjust our simulations to survey data in a Bayesian framework. This yields a family of likely posterior n(z) curves which quantifies the uncertainty of the measurement. Moreover, we develop a method for fast point spread function (PSF) estimation and modeling based on Deep Learning, specifically a convolutional neural network (CNN). Once trained, the computational speed of this algorithm allows it to be used within the MCCL framework to analyze large volumes of synthetic data. Based on the methods described above, we next present the first end-to-end application of the MCCL framework to survey data. In a non-tomographic setup, we constrain cosmology with cosmic shear using the DES Year (Y1) data. The core of our method is the joint measurement of the shear 2-point function and the associated redshift distribution. By simulating the full survey footprint numerous times, we quantify the systematic uncertainty of our analysis and are furthermore able to disentangle statistical and systematic errors. Building on this achievement, we implement a tomographic shear pipeline for the DES Year 3 (Y3) data. We classify galaxies into redshift bins with a machine-learning approach which enables us to measure tomographic shear 2-point functions along with the redshift distributions. The current results with this pipeline offer great prospects for applying the MCCL framework to current and future tomographic weak lensing datasets

Depth-sensitive time-of-flight small-angle neutron scattering

Block copolymers are quiet imported in industry. A detailed knowledge of the solid-liquid boundary conditions for surface effects in their aqueous solutions supports the development of smart coatings or the understanding of the folding of proteins in the vicinity of cell membranes. In this work, data collected from small-angle neutron scattering (SANS) experiments will be evaluated. The probed material is a 20\% (in weight) solution of the polymer Pluronic F127, which forms micelles inside the solution. The structures built by these micelles at different temperatures and different surface energies are the main topic of this work. It will be shown that SANS is an appropriate technique to probe solid-liquid boundaries depth-sensitively where the latter is a result of the use of a whole wavelengths spectrum instead of running the experiment at one fixed wavelength. The main result is that the micelles form a polycristalline fcc structure in case of an attractive surface potential. A repulsive potential suppresses crystallization up to a certain distance from the surface

Depth-sensitive time-of-flight small-angle neutron scattering

Block copolymers are quiet imported in industry. A detailed knowledge of the solid-liquid boundary conditions for surface effects in their aqueous solutions supports the development of smart coatings or the understanding of the folding of proteins in the vicinity of cell membranes. In this work, data collected from small-angle neutron scattering (SANS) experiments will be evaluated. The probed material is a 20\% (in weight) solution of the polymer Pluronic F127, which forms micelles inside the solution. The structures built by these micelles at different temperatures and different surface energies are the main topic of this work. It will be shown that SANS is an appropriate technique to probe solid-liquid boundaries depth-sensitively where the latter is a result of the use of a whole wavelengths spectrum instead of running the experiment at one fixed wavelength. The main result is that the micelles form a polycristalline fcc structure in case of an attractive surface potential. A repulsive potential suppresses crystallization up to a certain distance from the surface

Depth-sensitive time-of-flight small-angle neutron scattering

Block copolymers are quiet imported in industry. A detailed knowledge of the solid-liquid boundary conditions for surface effects in their aqueous solutions supports the development of smart coatings or the understanding of the folding of proteins in the vicinity of cell membranes. In this work, data collected from small-angle neutron scattering (SANS) experiments will be evaluated. The probed material is a 20\% (in weight) solution of the polymer Pluronic F127, which forms micelles inside the solution. The structures built by these micelles at different temperatures and different surface energies are the main topic of this work. It will be shown that SANS is an appropriate technique to probe solid-liquid boundaries depth-sensitively where the latter is a result of the use of a whole wavelengths spectrum instead of running the experiment at one fixed wavelength. The main result is that the micelles form a polycristalline fcc structure in case of an attractive surface potential. A repulsive potential suppresses crystallization up to a certain distance from the surface